Question

Find the value of angle B when we know the value of angle A, c, b

Answer 1

Use the cosine law to find the length of a:

`\begin{gathered} a^2=b^2+c^2-2bc\cos A \\ a=\sqrt[]{b^2+c^2-2bc\cos A} \end{gathered}`
`\begin{gathered} a=\sqrt[]{10^2+13^2-2(10)(13)\cos 33} \\ \\ a=\sqrt[]{100+169-260\cos 33} \\ \\ a=\sqrt[]{269-260\cos 33} \\ \\ a=\sqrt[]{50.94565233} \\ \\ a\approx7.13762 \end{gathered}`

Having the value of a, use sine law to find the measure of angle B:

`\begin{gathered} (\sin A)/(a)=(\sin B)/(b) \\ \\ \end{gathered}`
`\begin{gathered} b\cdot(\sin A)/(a)=\sin B \\ \\ B=\sin ^(-1)(b\cdot(\sin A)/(a)) \\ \\ B=\sin ^(-1)(10\cdot(\sin 33)/(7.13762)) \\ \\ B=49.734 \end{gathered}`Then, the measure of angle B is 49.734º